How do I only render what I see, excluding what I have hidden?
You need to select the filter in your scene view window, and make sure that the camera is enabled. This allows you to make certain objects not render in the viewport.
Bonus Tip:
If you have many different objects to turn off final render visibility on, select all objects you don't want to be rendered. Set the active object (yellow highlighted) in the scene viewer to be turned off in renders. Then once the camera icon is turned off for the active object, right click the icon and around the bottom of the pop up window, select copy to selected. This will set all other selected objects to have the same value as whatever you right clicked on. This also works for things like modifier settings, loc/rot/scale values, and much more.